Staking Plans with Simultaneous Bets

When placing a sports or race betting wager you are always confronted with two decisions:
(1) Which selection(s), if any, to back; and
(2) How much to wager on the selection(s) (i.e. how much to stake)

While the first decision plays a massive role in determining your long-term performance, the second decision is almost as important because a disciplined staking plan will help you to avoid losing money rapidly if you don’t have an edge over the bookmaker.

A staking plan, also referred to as bankroll management, is a formal methodology for choosing your stake amounts when placing bets. If you have $100 in your account and you’re dead certain a 1.50 odds selection will win, should you wager $1, $5, $20, $100?

The Introduction to Staking Plans outlined strategies such as Level Stakes, Percentage Stakes, Square Root Stakes, the Martingale and Reverse Martingale Strategies. The most common question we receive with these strategies is how to apply them when placing simultaneous bets. We define simultaneous here as when you place additional wagers before your first wager has concluded. While this issue doesn’t affect the Level Stakes plan (where you wager the same currency amount come rain or shine), it does impact the other plans.

Percentage Stakes and Square Root Stakes

For the sake of discussion we will use the Percentage Stakes and Square Root Stakes strategies to provide illustrative examples. You can learn more about them in the Staking Plans introduction, but for now, here are the basics of how they work. Note that the discussion below applies just as well to other staking plans.

Percentage Stakes

This plan simply involves setting a percentage of your account balance to wager on any given selection. For example, if your balance is $100 and you set a stake percentage of 5%, your next stake will be 0.05 * $100 = $5.00.

Square Root Stakes

This is similar to Percentage Stakes, except it incorporates more aggressive wagering once your account balance exceeds your deposit. When the account balance is equal to or below your initial deposit, you wager a set percentage of your account balance on each selection, just as you would using Percentage Stakes. If the account balance exceeds your deposit, however, you take the square root of the difference between your balance and the deposit, and add it to the set percentage of your account balance. For example, if you deposited $100, use a 5% wager percentage and and have a current balance of $125, your next wager will be √ ($125-$100) + ($125 * 0.05) = $5 + $6.25 = $11.25.

The Simultaneous Bets Conundrum

The above strategies are straightforward if you only place one wager at a time, however there’s no guidance on what to do when you place simultaneous wagers. For example, suppose you employ Percentage Stakes with a 5% rate and a $100 account balance. If you want to place five wagers at the same time, do you wager $5 on each bet? Or do you wager $5 on the first, then $95 * .05 = $4.75 on the second, $4.51 on the third and so on? Both options are risky, particularly if you place a large number of wagers at one time. With the first option you will have $25 at risk, which represents 25% of your entire account balance. The second option isn’t much better, putting 22.62% of your funds at risk. When placing a large number of simultaneous wagers, this approach leads to unintentionally high risk taking, which defeats the purpose of employing a staking plan that is designed to impose discipline.

Staking Plans with Simultaneous Bets

To employ simple staking systems such as Percentage Stakes or Square Root Stakes with simultaneous wagering, we recommend the following approach:

(1) Set a maximum percentage of your account balance to wager on any one selection (or event).
(2) Set a maximum percentage of your account balance to put at risk at any given time.

This will give you two numbers. The first determines the maximum stake per wager. The second determines the maximum total amount of funds at risk at any given time. When the two restrictions come into conflict you would choose the lower amount.

Suppose you set a maximum stake of 5% per wager but have another restriction that no more than 20% of your account balance can be at risk at any given time. If your starting balance is $100 and you wish to place just one bet you would wager $5.00. If, however your starting balance is $100 and you wish to place five bets then the 20% restriction would apply, because $5 x 5 is more than 20% of your account balance. In this case you would wager $20/5 = $4.00 per wager for your five bets.

If you are using the Square Root system and your current balance is $125 with an initial balance of $100, then if you make one wager your maximum stake is √ ($125-$100) + 0.05*$125 = $5 + $6.25 = $11.25.

Using the same $125 current balance and $100 initial balance, if you want to place five wagers with the 20% restriction applying, you would set your total risk level equal to √ (125-100) + 0.2*125 = $30.00. Each wager would then equal $6.00.

Staking Plans When You Already Have Funds at Risk

Using the Square Roots Stakes example above. Suppose you have $11.25 already at risk with one wager and you decide to place four additional wagers. Your current account balance is $125 – $11.25 = $113.75 plus you have $11.25 already at risk. Do you simply treat your account balance as $113.75 and set the following limits?:
Single wager: √ ($113.75 – $100.00) + 0.05*$113.75 = $9.40
Total at risk: √ ($113.75 – $100.00) + 0.2*$113.75 = $26.46

The problem with this approach is if you wager $26.46 on top of the previous bet of $11.25 you would have placed $37.71 at risk, which exceeds the $30 cap you set previously. Instead, we recommend using the following limits:
Single wager: √ ($125-$100) + 0.05*$125 = $5 + $6.25 = $11.25
Total at risk: $30.00 – $11.25 = $18.75

This approach ensures you never exceed the $30.00 cap that was in place prior to putting any funds at risk. If the single wager calculation causes you to exceed your $30 cap, you would instead wager the difference between your total cap and the amount of funds already at risk.

Limitations of Percentage Stakes and Square Root Stakes

The problem with simple strategies such as these is they don’t take into account whether you believe one bet is better value than another. They also don’t take into account each wager’s risk. They recommend the same stake regardless of whether the odds are 1.01 or 101.00.

Due to these limitations we recommend you use the stake calculations to determine the maximum stake you would consider wagering rather than the actual stake. You could then discount the stake based on bookmaker odds and/or a bet rating system.

The next section provides examples of how to adjust a simple staking plan to incorporate bookmaker odds and a bet rating system.